84 Schrodinger Equation Time-Independent
The stationary eigenvalue equation that is used to find the allowed energy levels and corresponding wavefunctions of a quantum system.
definition (Schrodinger Equation - Time-Independent) An eigenvalue equation used to determine the stationary states and quantized energy levels of a quantum system when the potential energy is independent of time. It determines the spatial part of the wave function \(\psi\) and the allowed energy values \(E\) that the system can possess. The generalized form is:
- \(\hat{H}\psi = E\psi\)
where
- \(\hat{H}\) is the Hamiltonian operator representing the total energy of the system.
- \(\psi\) is the spatial wave function.
- \(E\) is the energy of the state.
Note:
- \(\psi\) is lower-case psi.
- \(\psi\) is an eigenfunction of \(\hat{H}\).
- \(E\) is the corresponding eigenvalue.
84.1 References
- Hall, B. C. Quantum Theory for Mathematicians. Springer, 2013. — time-independent Schrödinger equation \(\hat{H}\psi = E\psi\). — source for the heading explanation.
- Absorption
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- Schrodinger Equation Time-Independent
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- Time Dependent Schrodinger Equation 1-Dimensional
- Time Dependent Schrodinger Equation Generalized
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